Convergence Properties of Genuine Bernstein–Durrmeyer Operators

Ana-Maria Acu ()
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Ana-Maria Acu: Lucian Blaga University of Sibiu, Department of Mathematics and Informatics

A chapter in Advances in Summability and Approximation Theory, 2018, pp 81-101 from Springer

Abstract: Abstract The genuine Bernstein–Durrmeyer operators have notable approximation properties, and many papers have been written on them. In this paper, we introduce a modified genuine Bernstein–Durrmeyer operators. Some approximation results, which include local approximation, error estimation in terms of the modulus of continuity and weighted approximation is obtained. Also, a quantitative Voronovskaya-type approximation will be studied. The convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.

Keywords: Genuine Bernstein–Durrmeyer operators; Rate of convergence; Linear positive operators; Voronovskaja-type theorem; 41A10; 41A25; 41A36 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-3077-3_5

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DOI: 10.1007/978-981-13-3077-3_5

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